Psychic is used in place of Psyshock because it's a better move.
- STAB is irrelevant because both moves are Psychic type so if you get STAB for one you get STAB for the other.
- Psychic is stronger with 90 instead of 80.
- Also Psychic has a chance to lower opponents special defence by one notch. Not that much of a perk but its better than nothing. Event if Psyshock was the same strength Psychic would still be overall better because of this small perk.
The only clear advantage to Psyshock is the move targets the opponents Defence instead of Special Defence. This means that Special Attacks have a way of defeating stronger Special Walls like Chansey for example, something Psychic might not do.
Think of Psyshock not as a replacement move for Psychic but as a replacement move for Zen Headbutt
- Targets defence instead of special defence like Zen Headbutt
- Better accuracy than Zen Headbutt
- Uses Special attack instead of attack which is usually desired on Psychic type Pokemon
To summarize: Psychic is a stronger and therefore usually better move. Psyshock is a good replacement for headbutt in attacking Pokemon with high special defence like Blissey.